Related papers: Convergence of Einstein Yang-Mills Systems
The Hamiltonian formulation of the theory of J-bundles is given both in the Hamilton--De Donder and in the Multimomentum Hamiltonian geometrical approaches. (3+3) Yang-Mills gauge theories are dealt with explicitly in order to restate them…
Recently, gauge field theory approaches were extensively used in order to discuss the physical consequences of spin-orbit interactions in condensed matter physics. An SU(2)$\times$U(1) gauge theory is very naturally borne out and provides…
In this paper we prove gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality. We apply the theorems to many examples of manifolds. We also prove a uniqueness theorem for the basic…
We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…
We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We…
We establish a general "boundedness implies convergence" principle for a family of evolving Riemannian metrics. We then apply this principle to collapsing Calabi-Yau metrics and normalized K\"ahler-Ricci flows on torus fibered minimal…
In [SW2], we defined a generalized mean curvature vector field on any almost Lagrangian submanifold with respect to a torsion connection on an almost K\"ahler manifold. The short time existence of the corresponding parabolic flow was…
In this paper, we introduce an \alpha -flow for the Yang-Mills functional in vector bundles over four dimensional Riemannian manifolds, and establish global existence of a unique smooth solution to the \alpha -flow with smooth initial…
With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many…
Supersymmetry provides a well-established theoretical framework for extensions of the standard model of particle physics and the general understanding of quantum field theories. We summarise here our investigations of N=1 supersymmetric…
New collective coordinates, related to the field at the `center' of the monopoles, are proposed. A systematic computation of the infrared properties of 2+1- and 3+1- dimensional Yang-Mills theory is now possible and is related to solutions…
Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a…
We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky and LeBrun in dimension four. We also improve the known…
A compactness theorem is proved for a family of K\"{a}hler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a…
We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to this…
Motivated by a conjecture of Donaldson and Segal on the counts of monopoles and special Lagrangians in Calabi-Yau 3-folds, we prove a compactness theorem for Fueter sections of charge 2 monopole bundles over 3-manifolds: Let $u_k$ be a…
We investigate relationship between a gauge theory on a principal bundle and that on its base space. In the case where the principal bundle is itself a group manifold, we also study relations of those gauge theories with a matrix model…
We study the existence of monopole bound states saturating the BPS bound in N=2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS…
The Han-Li conjecture states that: Let $(M,g_0)$ be an $n$-dimensional $(n\geq 3)$ smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant and $c$ be any real number, then there exists a conformal…
In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient inequality. We prove a Lojasiewicz-Simon…